Math. Finance Seminar WiSe 2025/2026

October 29, 2025, 2-4 pm, Location: A4-132 & A4-128

First Speaker:  Matthias Scherer (Technical University of Munich)

Title: Pricing Insurance Contracts with an Existing Portfolio as Background Risk

Abstract: How should an insurer price a new contract when it wants to account for the dependence between the new risk and its existing portfolio? This talk introduces a new premium principle—the conditional indifference premium—which explicitly incorporates the insurer’s current portfolio as background risk. Unlike classical law-invariant pricing rules, this approach captures the dependence between the new risk and existing exposures, yielding prices that better reflect diversification and accumulation effects.

The talk will present the theoretical foundations of the conditional indifference premium, explore its axiomatic and stochastic dominance properties, and highlight its connection to risk measures and regulatory capital. Through examples with exchangeable portfolios, we illustrate how portfolio size and dependence structure influence the marginal price of additional risks, shedding new light on the limits of diversification in insurance pricing.

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Second Speaker: Holger Kraft (Goethe University Frankfurt)

Title: Sustainable Decisions

Abstract: This paper rigorously defines sustainable decisions from first principles. A decision is sustainable if its performance (e.g., utility) constitutes at least a fair game. From a probabilistic point of view, this idea can be formalized by applying the concept of submartingales. Our approach allows us to establish the novel concept of sustainable optimization and leads to novel sustainable optimization and equilibrium problems. It requires an extension of the classical dynamic-programming paradigm including a formal derivation of a sustainable Bellman principle. Our approach can be applied to a huge number of decision problems where potentially heterogeneous decision makers optimize some form of "well-being" (e.g., utility or costs). We demonstrate its usefulness by studying various problems from economics, finance, marketing, or engineering. We derive sustainable consumption-investment strategies with habit formation or recursive utility, sustainable advertising strategies, sustainable compensation contracts in a principal-agent framework, or a sustainable equilibrium in a two-agent endowment economy. 

 

November 5, 2025, 2-3pm, Location: UHG H12

BGTS Colloquium

Speaker: Roxana Dumitrescu (ENSAE-CREST, Institut Polytechnique de Paris)

Title: Mathematical Modelling for a Sustainable Energy Future

Abstract: The environmental transition is one of the defining challenges of our time, and a key pillar in achieving it is the energy transition—the shift toward a cleaner, more efficient, and more flexible energy system. Within this context, demand side management plays a central role, relying on two complementary approaches: energy efficiency, which aims to reduce overall energy consumption, and demand flexibility, which enables consumers to adjust their usage in response to system needs.

In this talk, I will present two mathematical models that explore these approaches through the lens of incentives and interactions among large populations of consumers. Both models are developed using the frameworks of mean-field games and principal–agent mean-field games, powerful tools for analysing systems with many interacting decision-makers.

The first model focuses on demand flexibility, studying a scenario where consumers participate in a Demand Side Management contract and agree to reduce their aggregated power consumption by a predefined amount at random times. Numerical results illustrate how such  interactions influence consumption patterns and electricity prices.

The second model addresses energy efficiency, examining how an energy retailer can design innovative contracts based on a ranking system to encourage heterogeneous consumers to make lasting energy savings.

Together, these models shed light on how mathematical modelling can help design effective incentives and coordination mechanisms to support a sustainable energy future.

November 19, 2025, 2-4 pm, Location: A4-132 & A4-12

First Speaker:  Christa Cuchiero (University of Vienna)

Title: Generative AI for finance: modeling with neural and signature stochastic differential equations

Abstract: Generative AI has recently transformed a wide range of fields by enabling the modeling of complex and high-dimensional datasets as well as the synthesis of new content. In finance, it offers a modern approach to scenario generation, for instance through market simulators and return generators. This talk explores the key characteristics of generative AI models, including autoencoders, GANs, diffusion models, as well as neural and signature stochastic differential equations (SDEs) - with a particular focus on the latter two.

We delve into the mathematical foundations of neural and signature SDEs, emphasizing especially their universal approximation capabilities. As financial applications we present a Bayesian calibration approach to neural SDEs,  a data-driven version of the Heath–Jarrow–Morton framework for interest rate modeling, and signature-based asset price models calibrated jointly to VIX and SPX options.

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Second Speaker: Eduardo Abi Jaber (Ecole Polytechnique)

Title: Efficient Simulation of Affine Volterra Processes: From Heston to Hawkes

Abstract: We propose simple and efficient schemes for Affine Volterra processes, using integrated kernel quantities and the Inverse Gaussian distribution. The schemes preserve positivity, and can be shown to converge weakly by recasting them as stochastic Volterra equations with a measure-valued kernel. Our method applies to two important examples: Volterra square-root/Heston and Hawkes processes. In the first case, when using a fractional kernel, the scheme with large time steps seems to be more performant as the Hurst index H decreases to -1/2. In the second case, our scheme has deterministic complexity, in contrast with exact methods based on sampling jump times that have random complexity, which opens the door to efficient Monte Carlo methods.

 

 

December 3, 2025, 4-6 pm, Location: A4-132 & A4-128

First Speaker:  Eyal Neuman (Imperial College London)

Title: Stochastic Graphon Games with Memory

Abstract: We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals, that admit player-specific memory. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When interactions are modeled by a weighted graph, we formulate the corresponding continuum-player graphon game, and derive its Nash equilibrium explicitly using a novel approach. This approach consists of converting the first-order conditions into an infinite-dimensional coupled system of stochastic Fredholm equations, reducing it to an uncoupled system using the spectral decomposition of the graphon operator, and solving it in in closed form. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of players increases. Finally, we apply our results to various network games, including systemic risk models with delayed controls.

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Second Speaker: Martin Herdegen (University of Stuttgart)

Title: The Interplay between Utility and Risk in Portfolio Selection

Abstract: We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex risk measures such as Value at Risk.
Our main contribution is a novel and complete characterization of well-posedness for utility-risk portfolio selection in one period that takes the interplay between the utility and the risk objectives fully into account. We show that under mild regularity conditions the minimal necessary and sufficient condition for well-posedness is given by a very simple either-or criterion: either the utility functional or the risk functional need to satisfy the axiom of sensitivity to large losses. This allows to easily describe well-posedness or ill-posedness for many utility/risk pairs, which we illustrate by a large number of examples. The talk is based on joint work with Leonardo Baggiani and Nazem Khan.